Answer:
x = 5
Step-by-step explanation:
Using Pythagoras' identity.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.
Here the longest side, the hypotenuse is x + 8, thus
x² + (x + 7)² = (x + 8)² ← expand factors using FOIL
x² + x² + 14x + 49 = x² + 16x + 64
2x² + 14x + 49 = x² + 16x + 64 ← subtract terms on right side from both sides
x² - 2x - 15 = 0 ← in standard form
(x - 5)(x + 3) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
x + 3 = 0 ⇒ x = - 3
However x > 0 , thus x = 5
The sides of the right triangle are 5, 12, 13
